I have an Android phone. I’ve always had Android phones for some reason...price, probably!
Then, yes, you can get an app that will play MP3 files. You can copy files to the Android phone the same way you would to an MP3 player. I think you have to put them in the Music folder, but that’s easy.
If you want to spend money (and I know how you love to spend money) I think Google sells an unlimited streaming music service. I have no idea how much it costs. And, of course, if you have an unlimited data plan you can get the i heart radio app or something similar to stream music directly from the Internet.
1. There are free FM radio apps for Android phones search “top ten free fm radio apps Android”
2. If you have a computer you can copy your CD music to it as mp3 file then transfer your playlists to the phone, or copy from friends CDs